EQUIVALENT CIRCUIT MODEL FOR HIGH TEMPERATURE SUPERCONDUCTORS

Transcription

1 Lubl I E E E in University of Technology 5 th International Conference ELMECO Nałęczów, Poland September 2005 EQUIVALENT CIRCUIT MODEL FOR HIGH TEMPERATURE SUPERCONDUCTORS Dariusz Czerwiński, Leszek Jaroszyński Institute of Electrical Engineering and Electrotechnologies Lublin University of Technology ul. Nadbystrzycka 38A, Lublin, Poland darekc@weber.pol.lublin.pl, leszekj@weber.pol.lublin.pl Abstract Modern superconducting devices have many parts built of high temperature superconductors. An equivalent circuit model that describes the behaviour of a HTS superconductor viewed by an external user was proposed. From this point of view the most important quantities are voltage and current. The model is based on the physical structure and behaviour of HTS superconductors. Keywords: AC power losses, high temperature superconductors, PSpice ABM model INTRODUCTION High temperature superconductors operates at various conditions depending on the application solution. HTS parts are cooled with cryocooler or using cryogenic liquid. The energy losses in practical superconductor are very small under suitable working conditions. However during the quench process the amount of energy in HTS parts rapidly increases. The circuit model of HTS superconductor will improve the processes analysis during the transient states. For the purposes of model verification the transient analysis of HTS leads using PSpice environment was made. The simplicity of the model makes it fast and reliable. It is easy to obtain the results and compare them with the other ones based on finite element methods. Applied model is wide-ranging and may represent a HTS superconductor in different applications. HIGH TEMPERATURE SUPERCONDUCTORS The superconductors, because of their behaviour, can be divided into type I and type II. Type I superconductors have a clear border between superconducting state and resistivity state. Superconductors of type II have two values of critical magnetic flux -221-

2 density. High temperature superconductors are type II superconductors and the chemical structure of HTS are very specific (Fig. 1). All of HTS superconductors contain copper oxide walls, which act together with other elements as a active blocks conducting current. HTS superconductors contain also the defective regions. Forced current flow through defective regions may lead to a local quenching of superconductivity and the creation of so called hot spots. The deposited quench energy leads to a structural and chemical modification of the HTS material in the neighbourhood of these hot spots. Spreading of the quench zone may finally end up in the destruction of the superconductor. YBCO Bi 2212 Bi 2223 Fig. 1. Structures of HTS superconductors [1] First purpose of this model was the numerical analysis of the superconducting current lead built of BSCCO. Most of HTS current leads are prepared as ceramic tubes made of YBCO or BSCCO superconductors (Fig. 2). Fig. 2. Examples of HTS current leads It is possible to build the current lead basing on HTS tape. This type current leads are designed in CERN laboratory and are working in LHC project. Electro-thermal model of HTS tape vas verified with behaviour of real Bi-2223/Ag tapes leads. [2] -222-

3 ELECTRO-THERMAL HTS TAPE MODEL Electric properties of HTS superconductor tape can be described in a simplified form as shown in Fig. 3. Fig. 3. Equivalent circuit of HTS tape Silver alloy resistance can be calculated using equation (1): R Ag Ag ( T ) L (1) A Ag where: Ag( T ) at b silver alloy resistivity; a, b constants [2]; L tape length; A Ag silver alloy cross-section area. Superconductor resistance can be calculated using formula (2): E L n 1 R R i (2) Bi res C n IC where: R res SC residual resistance; E C = 10-4 T V/m; n n 0 0 SC n-exponent; T T n 0 n-exponent at temperature T 0 ; C T I C IC0 SC critical current (at self field); TC T0 I C0 critical current at T 0 ; T C critical temperature. Thermal properties of HTS tape in adiabatic condition can be described by the equivalent circuit shown in Fig. 4. Fig. 4. Simplified thermal equivalent circuit of HTS tape -223-

4 (3). Uniform HTS tape temperature in adiabatic condition can be calculated using formula t1 1 T T0 ( utape itape)dt (3) C TH t0 where: CTH mbicpbi magcpag thermal capacity; T 0 ambient temperature;m Bi superconductor mass; C pbi superconductor specific heat; m Ag silver alloy mass; C pag silver alloy specific heat; u tape, i tape tape voltage and current. HTS electro-thermal equivalent circuit made of analogue behavioural blocks is presented in Fig. 5. Fig. 5. Equivalent circuit for Bi2223/Ag tape and its simulation parameters (PSpice ABM blocks: 1, 2, 3 voltage-controlled voltage sources; 4, 5 voltage-controlled current sources) Simulation parameters compiled from [2, 3, 4] are described in Table 1. Table 1. Bi(Pb)-2223/AgAg tape simulation parameters I C0 (77 K, self field) 57 A R res Ω T C 106 K a Ωm/K A TAPE 3.81 x mm 2 b Ωm L 1 m C pbi 120 J/(kg K) filling factor 30 % C pag 170 J/(kg K) E C 10-4 V/m γ Bi 6000 kg/m 3 n 0 (77 K) 15 γ Ag kg/m

5 NUMERICAL SIMULATION RESULTS Transient analysis of electro-thermal HTS tape model has been carried out using PSpice. Selected results of the numerical analysis are presented in Fig. 6 and Fig V 78V 76V 100W V(T) 50W 0W 1.0V (I(Ag)+ I(sc))*V(Tape) 0V -1.0V 200A V(Tape) 0A SEL>> -200A 0s 20ms 40ms 60ms 80ms 100ms I(Ag)+ I(sc) I(Ag) I(sc) Time Fig. 6. Temperature, instantaneous power, voltage, current of HTS tape under sinusoidal over-current 150 A peak 120V 100V 80V 60V 2.0KW V(T) 1.0KW 0W 4.0V (I(Ag)+ I(sc))*V(Tape) 0V SEL>> -4.0V 400A V(Tape) 0A -400A 0s 20ms 40ms 60ms 80ms 100ms I(Ag)+ I(sc) I(Ag) I(sc) Time Fig. 7. Temperature, instantaneous power, voltage, current of HTS tape under sinusoidal over-current 300 A peak -225-

6 CONCLUSION Physical properties of HTS superconductors vary in a wide ranges and their relation to the temperature, current and magnetic filed is very difficult for implementation in circuit model representation. AC current overload of HTS superconductors is noticeable but normal resistance develops rapidly when the amplitude of over-current is over three times of the critical current. Numerical model might be improved: it s necessary to use proper relation between HTS tape specific heat and temperature especially in low temperature range (T < 20 K). Simulation results show good correlation with experimental results [2]. It s possible to use presented in this paper numerical model for simulation of electrothermal properties of HTS materials in different applications. REFERENCES [1] Oomen, Marijn Pieter, AC loss in superconducting tapes and cables, Eerste Uitgave 2000, Universiteit Twente [2] Seong-Woo Yim, Sung-Hun Lim, Hye-Rim Kim Si-Dole Hwang, Kohji Kishiro, Electrical Behavior of Bi-2223/Ag Tapes Under Applied Alternating Over-Currents, IEEE Transactions on Applied Superconductivity, vol. 15, No. 2, June 2005 [3] Y. S. Cha, Semi-Empirical Correlation for Quench Time of Inductively Coupled Fault Current Limiter, IEEE Transactions on Applied Superconductivity, vol. 15, No. 2, June 2005 [4] T. J. Arndt, A. Aubele, H. Krauth, M. Munz, B. Sailer, Progress in preparation of technical HTS tapes of type Bi-2223/Ag alloy of industrial lengths, IEEE Transactions on Applied Superconductivity, vol. 15, No. 2, June